Condensed Matter > Strongly Correlated Electrons

Title:Signatures of rare states and thermalization in a theory with confinement

Abstract: There is a dichotomy in the nonequilibrium dynamics of quantum many body
systems. In the presence of integrability, expectation values of local
operators equilibrate to values described by a generalized Gibbs ensemble,
which retains extensive memory about the initial state of the system. On the
other hand, in generic systems such expectation values relax to stationary
values described by the thermal ensemble, fixed solely by the energy of the
state. At the heart of understanding this dichotomy is the eigenstate
thermalization hypothesis (ETH): individual eigenstates in nonintegrable
systems are thermal, in the sense that expectation values agree with the
thermal prediction at a temperature set by the energy of the eigenstate. In
systems where ETH is violated, thermalization can be avoided. Thus establishing
the range of validity of ETH is crucial in understanding whether a given
quantum system thermalizes. Here we study a simple model with confinement, the
quantum Ising chain with a longitudinal field, in which ETH is violated.
Despite an absence of integrability, there exist rare (nonthermal) states that
persist far into the spectrum. These arise as a direct consequence of
confinement: pairs of particles are confined, forming new `meson' excitations
whose energy can be extensive in the system size. We show that such states are
nonthermal in both the continuum and in the low-energy spectrum of the
corresponding lattice model. We highlight that the presence of such states
within the spectrum has important consequences, with certain quenches leading
to an absence of thermalization and local observables evolving anomalously.